Piezoelectric accelerometer

ABSTRACT

At least some of the example embodiments are methods including measuring motion of a body by deflecting a first cantilever portion of a sensing element, and deflecting a second cantilever portion of a sensing element, the second cantilever element of the sensing element disposed opposite the first cantilever element. A first voltage having a first polarity is created across electrical leads responsive to the deflecting of the cantilever portions opposite the direction of the first acceleration of the body. The sensing element is supported by way of a mounting plate medially disposed on the sensing element.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.15/264,231 filed Sep. 13, 2016 titled “Piezoelectric Accelerometer.” TheSer. No. 15/264,231 is a divisional of U.S. patent application Ser. No.14/145,093 filed Dec. 31, 2013 titled “Piezoelectric Accelerometer” (nowU.S. Pat. No. 9,470,806). The Ser. No. 14/145,093 claims priority toU.S. Provisional Patent Application Ser. No. 61/871,482 filed Aug. 29,2013. All the noted applications incorporated by reference as ifreproduced in full below.

BACKGROUND

Geophysical surveying (e.g., seismic, electromagnetic) is a techniquewhere two- or three-dimensional “pictures” of the state of anunderground formation are taken. Geophysical surveying takes place notonly on land, but also in marine environments (e.g., ocean, largelakes). Marine geophysical survey systems use a plurality of sensorstreamers (long cables), which contain one or more sensors to detectacoustic energy emitted by one or more sources and reflected from theunderground formation. Detection and interpretation of the signalsrepresented thereby can be attenuated by destructive interference withreflections of the energy from interfaces present in the marineenvironment, particularly the water-air interface at the surface.

Discrimination against reflected signals may be provided by combiningsignals from multiple detector types sensitive to different physicalcharacteristics of the acoustic signal. For example, when appropriatelycombined, the output from hydrophones sensitive to the pressureperturbation from the acoustic signal may be used in conjunction withthe output of a detector sensitive to the velocity of a fluid particlefor example, a geophone, may provide such discrimination. However, thesedetectors, particularly the geophone, typically are complex andconcomitantly, costly to manufacture. Thus a low-cost device which maybe used to provide similar capabilities would provide a competitiveadvantage in the marketplace.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed description of exemplary embodiments, reference will nowbe made to the accompanying drawings in which:

FIG. 1A shows, in an exploded view, an accelerometer in accordance withat least some embodiments;

FIG. 1B shows, in a perspective view an accelerometer in accordance withat least some embodiments;

FIG. 1C shows, in a top section view an accelerometer in accordance withat least some embodiments;

FIG. 2A shows in a perspective view, a housing in accordance with atleast some embodiments;

FIG. 2B shows, in a top section view, a housing in accordance with atleast some embodiments;

FIG. 3A shows, in a perspective view, a piezoelectric sensing element inaccordance with at least some embodiments;

FIG. 3B shows, in a side elevation view, a piezoelectric sensing elementin accordance with at least some embodiments;

FIG. 4A shows, in a perspective view, a mounting plate in accordancewith at least some embodiments;

FIG. 4B shows, in a front elevation view, a mounting plate in accordancewith at least some embodiments;

FIG. 5A shows, in a perspective view and front elevation an end plate inaccordance with at least some embodiments;

FIG. 5B shows, in a front elevation view, an end plate in accordancewith at least some embodiments;

FIG. 6A shows in a front elevation view, and side elevation a cap inaccordance with at least some embodiments;

FIG. 6B shows in a side elevation view, a cap in accordance with atleast some embodiments;

FIG. 7 shows a schematic front elevation of a piezoelectric sensingelement in accordance with at least some embodiments;

FIG. 8 shows a transverse section view of an accelerometer in accordancewith at least some embodiments; and

FIG. 9 shows an overhead view of a marine survey system in accordancewith at least some embodiments;

FIG. 10 shows a flow diagram of a method in accordance with at leastsome embodiments.

NOTATION AND NOMENCLATURE

Certain terms are used throughout the following description and claimsto refer to particular system components. As one skilled in the art willappreciate, different companies may refer to a component by differentnames. This document does not intend to distinguish between componentsthat differ in name but not function. In the following discussion and inthe claims, the terms “including” and “comprising” are used in anopen-ended fashion, and thus should be interpreted to mean “including,but not limited to . . . ” Also, the term “couple” or “couples” isintended to mean either an indirect or direct connection. Thus, if afirst device couples to a second device, that connection may be througha direct connection or through an indirect connection via other devicesand connections.

“Cable” shall mean a flexible, load carrying member that also compriseselectrical conductors and/or optical conductors for carrying powerand/or signals between components.

“Marine environment” shall mean an underwater location regardless of thesalinity of the water. Thus, even an underwater location in a body offresh water shall be considered a marine environment.

“Fluid particle” shall mean a small amount of fluid which may beidentifiable while moving with a fluid flow; a fluid particle may alsobe referred to as a fluid element. In some embodiments, “fluid particle”may be specifically interpreted to mean any fluid parcel that is smallerthan about one-tenth wavelength of sound in a medium in any direction,and, for example, in at least some embodiments may be less than 0.75 min any direction.

“Transect” shall mean to subdivide or partition into separatelyidentifiable portions, but not necessarily into physically disjointportions.

“Exemplary,” as used herein, means serving as an example, instance, orillustration.” An embodiment described herein as “exemplary” is notnecessarily to be construed as preferred or advantageous over otherembodiments.

The terms “upper” and “lower” shall be considered relative locationalterms in view of the local force of gravity and a particular orientationof a device, but shall not be read to require a particular operationalorientation of the device.

DETAILED DESCRIPTION

The following discussion is directed to various embodiments of theinvention. Although one or more of these embodiments may be preferred,the embodiments disclosed should not be interpreted, or otherwise used,as limiting the scope of the disclosure or the claims. In addition, oneskilled in the art will understand that the following description hasbroad application, and the discussion of any embodiment is meant only tobe exemplary of that embodiment, and not intended to intimate that thescope of the disclosure or the claims, is limited to that embodiment.

The various embodiments are directed to an accelerometer which may beused to detect fluid particle accelerations and thereby, by integration,fluid particle velocities in conjunction with marine geophysical surveysystems. Although the developmental context may be marine geophysicalsurvey, embodiments of the accelerometer in accordance with theprinciples disclosed herein are of general applicability and may be usedin other applications where a determination of an acceleration of a bodyis desired. When used in the context of a marine geophysical survey,measurements of fluid particle velocity can be used to predictproperties of formations below a body of water. In particular,measurements of fluid particle velocity may assist in identifying thelocation of hydrocarbon-bearing reservoirs in the formations.

FIGS. 1A and 1B show perspective views of an accelerometer 100 inaccordance with at least some embodiments. Turning first to FIG. 1A, anexploded perspective view of an accelerometer 100 is shown.Accelerometer 100 includes a sensor 102. In at least some embodiments,sensor 102 comprises a piezoelectric sensing element 104 disposed withinmounting plates 106. Together, piezoelectric sensing element 104 andmounting plates 106 comprise a centrally supported beam. Mounting plates106 transect piezoelectric sensing element 104 into two cantileverportions 105 and a central portion 107 disposed between mounting plates106. Mounting plates 106 abut an interior wall of housing 114. Theembodiment of accelerometer 100 shown in FIG. 1A includes a pair ofmounting plates 106, however alternative embodiments may employ a singlemounting plate 106. In such embodiments, a single mounting plate maytransect piezoelectric sensing element 104 into two cantilever portionswithout a central portion. Piezoelectric sensing element 104 will bedescribed in further detail in conjunction with FIG. 3. As describedfurther below in conjunction with FIGS. 3 and 7, the centrally supportedbeam architecture of the piezoelectric sensing element 104 and mountingplates 106 form a spring-mass system which may be responsive toaccelerations of accelerometer 100.

Mounting plates 106 may also be configured to provide electricalcoupling of signals generated by piezoelectric sensing element 104 toexternal circuitry (not shown in FIG. 1) via wires 108. In anembodiment, mounting plates 106 may be formed from printed circuit boardmaterial. An embodiment of a plate that may be used in conjunction withaccelerometer 100 will be described in further detail in conjunctionwith FIG. 4. Wires 108 may, in some embodiments, be bare conductors, andin alternative embodiments may comprise insulated conductors. Wires 108may couple to external circuitry via end plate 110 and external wires112. External wires 112 may be comprised of insulated conductors.However, it would be understood by those skilled in the art that in atleast some embodiments in which other mechanisms to avoid the shortingof external wires 112 are provided, wires 112 may be comprised of bareconductors.

Piezoelectric sensing element 104 may be disposed within housing 114.Housing 114 may comprise a circular cylinder forming openings 113A, 113Bin corresponding ends 115A, 115B. Housing 114 further defines aninternal volume 117 (partially obscured in FIG. 1A) for receivingpiezoelectric sensing element 104. Piezoelectric sensing element 104 maybe received in internal volume 117 via opening 113A. Housing 114 may beany suitable material sufficient to protect piezoelectric sensingelement 104 from damage when accelerometer 100 is deployed. Housing 114may, for example, be comprised of a metal shell formed from materials asbrass, copper or aluminum. An embodiment of housing 114 which may beused in conjunction with accelerometer 100 is shown in further detail inFIG. 2. In at least some embodiments, housing 114 may be omitted orreconfigured with other cross-sectional shapes, such as rectangles,triangles, etc. End plate 110 may be fixedly attached to housing 114. Inembodiments of housing 114 formed from a metal, attachment of end plate110 to housing 114 may be by soldering. Alternatively, attachment may beeffected by an adhesive. Housing 114 may be closed by cap 116 which maybe received in opening 113B. Cap 116 may be comprised of the same ordifferent material than housing 114 and may be fixedly attached theretoby soldering (in embodiments comprised of a solderable metal) or,alternatively, by an adhesive. Note that in some embodiments ofaccelerometer 100, cap 116 may be omitted, for example, in deploymentswherein environmental exposure of accelerometer 100, and, in particularpiezoelectric sensing element 104, is not of concern.

FIG. 1B shows a perspective view of an assembled accelerometer 100 inaccordance with at least some embodiments. In FIG. 1B, housing 114,external wires 112 and cap 116 are visible as in FIG. 1A. Additionally,potting 118 may be disposed in the end of housing 114 proximal to theexternal wires thereby sealing such end and insulating the connectionsbetween external wires 112 and end plate 110 (not shown in FIG. 1B).Potting 118 may comprise a potting compound such as HMP-85 from ChaseCorporation, however, other potting compounds may also be employed.

Refer now to FIG. 1C. FIG. 1C shows a cross sectional view ofaccelerometer 100 along the section 1C-1C in FIG. 1B. Piezoelectricsensing element 104 may be disposed within interior volume 117 ofhousing 114. Potting 118 is shown in further detail and abutting endplate 110. As depicted in the illustrated embodiment of accelerometer100, cap 116, housing 114 and potting 118 form a sealed enclosure forpiezoelectric sensing element 104. Further, in an embodiment in whichhousing 114 comprises a metallic structure, the outside diameters orcircumferences 120 of mounting plates 106 may also comprise a solderablematerial and circumferences 120 may be attached to an interior wall 122of housing 114 by soldering thereto. Likewise, an outside diameter orcircumference 124 of end plate 110 and a circumference 126 of cap 116may also be attached to housing 114 by soldering.

FIG. 2 shows an embodiment of housing 114 in further detail, in twoviews: a perspective view, FIG. 2A and a cross-sectional view alongsection 2B-2B in the perspective view, FIG. 2B. The inside diameter orinterior wall 122 of housing 114 bounds interior volume 117 and mayinclude a counter bore 202 that defines an annular shoulder region 204.Openings 115A, 115B further define the extent of interior volume 117.Counter bore 202 forms shoulder region 204 where it abuts the remainingportion of interior wall 122. Shoulder region 204 may mate withcircumference 124 of end plate 110 (not shown in FIG. 2) thereto asillustrated in FIG. 1C, and may be fixedly attached thereto bysoldering, for example. A scribed score or similar marking such as anindentation or paint line (not shown on FIG. 2) may be provided on theexterior of housing 114 parallel to its longitudinal axis and alignedwith piezoelectric sensing element 104 to facilitate orienting theaccelerometer.

Refer now to FIG. 3 showing, in perspective, FIG. 3A and end view, FIG.3B, a piezoelectric sensing element 104 in accordance with at least someembodiments of the principles set forth herein. Piezoelectric sensingelement 104 includes a pair of piezoelectric plates 302A and 302B,adhesive layers 304 disposed between piezoelectric plates 302A, 302B andconducting plate 306. In at least some embodiments, piezoelectric plates302A and 302B may be substantially rectangular, although othergeometries may also be used in alternative embodiments. Further,piezoelectric plates may be disposed having a substantially congruentrelationship therebetween. Piezoelectric plates 302A and 302B may becomprised of a ceramic piezoelectric material, such as, for example,lead titanate zirconate (PZT). As would be understood by one of ordinaryskill in the art with the benefit of this disclosure, piezoelectricmaterials exhibit an electric charge when subject to mechanical stressand, conversely, exhibit a mechanical strain when subject to an electricpotential. Thus, a piezoelectric material subject to an acceleration andthereby a force in accordance with the laws of mechanics may exhibit anelectric charge in response thereto. Piezoelectric plates 302A and 302Bmay, in at least some embodiments, be comprised of APC 850 material fromAPC International, Ltd., which is a PZT-based material. Otherpiezoelectric materials, for example, barium titanate (BaTiO₃), leadtitanate (PbTiO₃), zinc oxide (ZnO), sodium potassium niobate((K,Na)NbO₃), bismuth ferrite (BiFeO₃), sodium niobate (NaNbO₃), bismuthtitanate (Bi₄Ti₃O₁₂), sodium bismuth titanate (Na_(0.5)Bi_(0.5)TiO₃),berlinite (AlPO₄), barium sodium niobate (Ba₂NaNb₅O₁₅), lead potassiumniobate (Pb₂KNb₅O₁₅), quartz, Rochelle salt or plastic piezoelectricmaterials such as polyvinylidene fluoride (PVDF) may be used inalternative embodiments of piezoelectric sensing element 104. Conductingplate 306 may be comprised of copper, brass, or other metallic material.Adhesive layers 304 may be comprised of an epoxy adhesive. An exemplaryepoxy adhesive which may be used in an embodiment of piezoelectricsensing element 104 is LOCTITE® E-30CL epoxy structural adhesive fromHenkel Corporation. Further, in alternative embodiments of piezoelectricsensing element 104, adhesive layers 304 may be omitted, and in yetother alternative embodiments, conducting plate 306 may be omitted, andin still other alternative embodiments both adhesive layers 304 andconducting plate 306 may be omitted.

Considering further piezoelectric plates 302A and 302B, piezoelectricplates 302A, 302B may have disposed on a face 308 thereof a conductingmaterial to facilitate the attachment of mounting plates 106 asdescribed in conjunction with FIG. 1 above. For example, faces 308 maycomprise silvered surfaces. In some embodiments, faces 308 may compriseother metals, for example electroless nickel, or gold. Further still,piezoelectric plates 302A and 302B may be polarized. For example, in anembodiment, piezoelectric plates 302A and 302B may have an electricpolarization, P, in a direction substantially perpendicular to faces308, shown as the y-direction in FIG. 3. In at least some embodiments,piezoelectric plates 302A and 302B may be arranged such that therespective polarizations, P, are oppositely directed, whereby forexample, in piezoelectric plate 302A, P may be substantially directed inthe positive y-direction, and in piezoelectric plate 302B, P may besubstantially directed in the negative-y direction. Such a dispositionof plates 302A and 302B may be referred to a series mode operation.Series mode operation will be described further below in conjunctionwith FIG. 7. Although the illustrated embodiment of piezoelectricsensing element 104 employs two piezoelectric plates, piezoelectricsensing element 104, in at least some embodiments, may be comprised of asingle plate, wherein faces 308 comprise opposite faces of the singleplate.

Refer now to FIG. 4 showing in further detail an exemplary mountingplate 106 which may be used in conjunction with an embodiment ofaccelerometer 100. FIG. 4 depicts mounting plate 106 in perspective,FIG. 4A, and front elevation view, FIG. 4B. Mounting plate 106 includesa slot 402 configured to receive piezoelectric sensing element 104 asdescribed above in conjunction with FIGS. 1A-C, and conducting traces404 which may serve to solderably attach to piezoelectric sensingelement 104 via a portion 405 abutting slot 402. Thus, for example, ajoint may be formed between portion 405 and a silvered face 308 ofpiezoelectric element 104 by the application of a eutectic compositionof paste solder at the junction of portion 405 and face 308. The pastesolder may be of the type used in surface-mount construction. The jointmay then be formed by application of heat at a low temperature, e.g.just sufficient to melt the paste solder, using a soldering tool withlarge thermal mass such that the temperature of the tool is notmaterially reduced by the heat lost in melting the solder. Inalternative embodiments, the joint may be formed using a conductingadhesive, and in yet other embodiments, an adhesive and embeddedconducting wire may be used.

Additionally, conducting traces 404 may also serve to electricallyconnect wires 108 to piezoelectric sensing element 104, via holes 407.Holes 407 may extend through a thickness of mounting plate 106 and maybe plated through to form an electrical connection to conducting traces404, and may be configured to receive ends of wires 108. Mounting plate106 may further comprise conducting traces 406 disposed at an outsidediameter thereof. In embodiments of housing 114 comprised of a metallicshell, conducting traces 406 may serve as solderable attachmentsthereto. In at least some embodiments, mounting plate 106 may becomprised of a circular disk, and further, in some embodiments, aportion of a circular disk. Thus, the periphery of mounting plate 106may include arcuate surfaces 408, which in at least some embodiments maybe defined by circular arcs 409. Surfaces 408 may abut interior wall 122of housing 114. Additionally, in at least some embodiments, theperiphery of mounting plate 106 may be additionally comprised of linearsurfaces 410 which may be defined by chords 411. In at least someembodiments, mounting plate 106 may be fabricated of glass-reinforcedepoxy laminate material, for example FR4 glass laminate printed circuitboard material.

Referring now to FIG. 5, there is shown an exemplary embodiment of endplate 110 which may be used in conjunction with accelerometer 100. FIG.5 shows a perspective, FIG. 5A, and front elevation view, FIG. 5B, ofend plate 110. End plate 110 includes conductive traces 502. Holes 504Aand 504B may extend through a thickness of end plate 110 and beconfigured to receive ends of wires 112 and 108, respectively. Holes504A and 504B may comprise plated-through holes, and may furthercomprise solderable connections to wires 112 and 108. End plate 110 mayalso include conductive trace 506 disposed at the outside diameter ofend plate 110. In embodiments of housing 114 comprised of a metallicshell, conducting trace 506 may serve as a solderable attachmentthereto. In at least some embodiments, end plate 110 may have an outsidediameter of about 14 mm. Further, in at least some embodiments, endplate 110 may be fabricated of a glass-reinforced epoxy laminatematerial, for example FR4 glass laminate printed circuit board material.

FIG. 6 shows an exemplary embodiment of a cap 116 which may be used inconjunction with accelerometer 100. FIG. 6A shows a front elevation viewand FIG. 6B a side elevation view of cap 116. A diameter of periphery602 of cap 116 may have a diameter sufficient to enclose an end ofhousing 114. Flange portion 604 may have a diameter sized to mate withan inside diameter of housing 114. In embodiments of housing 114comprised of a metallic shell, the diameter of flange portion 604 may befurther sized to form a solderable attachment to housing 114. In otherembodiments, an adhesive may be used to form the attachment. Aspreviously discussed, in at least some embodiments of accelerometer 100,cap 116 may be omitted as, for example, in deployments of accelerometer100 in which sealing of piezoelectric sensing element 104 from exposureto foreign matter is not an issue. In at least some embodiments,periphery 602 may have a diameter of about 14.5 mm. Further, in at leastsome embodiments flange portion 604 may have a diameter of about 13.6mm. The dimensions set forth herein are exemplary and other dimensionsmay be used in conjunction with embodiments of accelerometer 100deployed in various applications. Cap 116 may be comprised of a metal,and in at least some embodiments may comprise, for example, brass orcopper.

To further understand the operation of an accelerometer in accordancewith the principles of the disclosure refer now to FIG. 7. FIG. 7schematically illustrates the displacement of piezoelectric sensingelement 104 subject to an acceleration along the y-axis in thenegative-y direction. In at least some embodiments of accelerometer 100,the y axis may be the desired axis of sensitivity, wherein the responseof the accelerometer to components of an applied acceleration along, forexample, axes mutually perpendicular to the y axis, is relatively small.For the purposes of illustration, the displacements are exaggerated inFIG. 7. The flexural response of piezoelectric sensing element 104 tosuch acceleration comprises a compression of the upper portion thereofgoing into compression in the x direction and the lower portion ofpiezoelectric sensing element 104 going into tension in the x direction.In an embodiment of piezoelectric sensing element 104 configured forseries mode operation, the opposite polarization of piezoelectric plates302A and 302B, the complementary stresses can produce a net chargedisplacement which manifests itself as an output voltage signalproportional to the y component of the displacement of cantileverportions 105. In conjunction with its own mass, the flexural springconstant of piezoelectric sensing element 104 forms a “spring-masssystem.” As such, it may exhibit a resonant frequency in the flexuralmode. At frequencies below such resonant frequency, the lateral stressesin the x-direction resulting from flexure of piezoelectric sensingelement 304 may be proportional to the component of acceleration alongthe y axis. In an embodiment including two piezoelectric plates 302A,302B comprising APC 850 each having exemplary dimensions of about 27 mmlength (x-axis), by about 10 mm width (z-axis) and 0.25 mm thickness(z-axis) and a conducting plate 306 comprised of brass disposedtherebetween and having a thickness of 0.2 mm, the flexural moderesonant frequency may be about 2.3 kHz. Considering an embodimentdeployed in a marine environment, such a resonant frequency is above theband of frequencies generated by seismic sources. The resonant frequencymay be adjusted by, for example, the attachment of weights to cantileverportions 105 of piezoelectric sensing element 104. The dimensions setforth herein are exemplary and other dimensions may be used inconjunction with embodiments of accelerometer 100 deployed in variousapplications.

Considering further a marine environment, accelerations induced by theseismic signal fluid particle motion are generated by an acousticpressure wave. As would be understood by one of ordinary skill in theart with the benefit of this disclosure, the magnitude of the pressurewave relative to the magnitude of the acceleration of the fluid particleis inversely proportional to the frequency of the pressure wave.Generally, pressure is a scalar and acts isotropically over the surfaceof housing 114. FIG. 8 shows a simplified transverse section throughaccelerometer 100 to illustrate the action of a pressure wave thereon.The pressure acting on accelerometer 100 is depicted by arrows 802. Thepressure is supported in part by the hoop stiffness of housing 114. Aslight decrease in the circumference of housing 114 may result therefromproducing stress in they and z directions in piezoelectric sensingelement 104. The electrical output of piezoelectric sensing element 104may be a function of the amount of stress and its direction relative tothe axis of polarization of the piezoelectric material comprisingsensing element 104. As discussed above, in at least some embodiments,the polarization may be along the y axis. In such embodiments, acompressive stress along the z axis will produce a positive displacementof charge and a compressive stress along the y axis will produce anegative displacement of charge. However, because of the orthotropicnature of piezoelectric material, these counter-polarized displacedcharges may not have the same amplitude and therefore may not cancel(algebraically sum to zero). In at least some embodiments, mountingplate 106 may, as described above in conjunction with FIG. 4, have aperimeter comprising circular arcs 409 and chords 411. The stressdistribution in the y-z plane may thereby be modified such that theratio of the pressure-induced stresses in the y and z directions arescaled wherein the charges respectively displaced are both opposite insign and substantially equal in magnitude. Consequently, in suchembodiments, the counter-polarized charges may substantially cancel, andin such embodiments, the acoustic pressure sensitivity may besubstantially reduced. Additionally, by way of example, considering they axis to be the desired axis of sensitivity, the sensitivity ofaccelerometer 100 to rotations about the y axis may be further reducedin embodiments of accelerometer 100 comprising a pair of mounting plates106. Such an exemplary embodiment has been described above inconjunction with FIG. 1. As described in conjunction with FIG. 7,flexural deflections of cantilever portions 105 may generatepiezoelectric charge displacements to further provide an output signalfrom sensing element 104. It is further noted that a rotation ofpiezoelectric sensing element 104 about the z axis, which may be inducedby a rotation of accelerometer 100, may produce an out-of-phase flexureof cantilever portions 105, that is, a flexure in which thedisplacements of the cantilever portions are oppositely directed (notshown in FIG. 7). The resulting stresses may comprise a compressivestress in one of the cantilever portions 105 and a tensile stress in theother. The piezoelectric charge displacements may then be of oppositesign and may substantially cancel, thereby rendering accelerometer 100substantially insensitive to such rotations about the z axis.

Still considering a marine environment deployment, FIG. 9 shows anoverhead view of a marine survey system 900 in accordance with at leastsome embodiments. In particular, FIG. 9 shows a survey vessel 902 havingonboard equipment 904, such as navigation, energy source control, anddata recording equipment. Survey vessel 902 is configured to tow one ormore streamers 906A-F through the water. While FIG. 9 illustrativelyshows six streamers 906, any number of streamers 906 may be used. Thediscussion continues with respect to streamers 906 being sensorstreamers, but streamers 906 are illustrative of any towed geophysicalsurvey cable, such as transmitter cables and source cables.

The sensor streamers 906 are coupled to towing equipment that maintainsthe streamers 906 at selected depth and lateral positions with respectto each other and with respect to the survey vessel 902. The towingequipment may comprise two paravane tow lines 908A and 908B each coupledto the vessel 902 by way of winches 910A and 9106, respectively. Thewinches enable changing the deployed length of each paravane tow line908. The second end of paravane tow line 908A is coupled to a paravane912, and the second end of paravane tow line 908B is coupled to paravane914. In each case, the tow lines 908A and 908B couple to theirrespective paravanes through respective sets of lines called a “bridle”.The paravanes 912 and 914 are each configured to provide a lateral forcecomponent to the various elements of the survey system when theparavanes are towed in the water. The combined lateral forces of theparavanes 912 and 914 separate the paravanes from each other until theparavanes put one or more spreader lines 920, coupled between theparavanes 912 and 914, into tension. The paravanes 912 and 914 eithercouple directly to the spreader line 920, or as illustrated couple tothe spreader line by way of spur lines 922A and 922B.

The sensor streamers 906 are each coupled, at the ends nearest thevessel 902 (i.e., the proximal ends) to a respective lead-in cabletermination 924A-F. The lead-in cable terminations 924 are coupled to orare associated with the spreader lines 920 so as to control the lateralpositions of the streamers 906 with respect to each other and withrespect to the vessel 902. Electrical and/or optical connections betweenthe appropriate components in the recording system 904 and the sensors(e.g., 916A, 916B) in the streamers 906 may be made using inner lead-incables 926A-F. Much like the tow lines 908 associated with respectivewinches 910, each of the lead-in cables 926 may be deployed by arespective winch or similar spooling device such that the deployedlength of each lead-in cable 926 can be changed.

Sensors 916A, 916B may include one or more instruments to detect seismicsignals which may be generated by a source, such as an air gun or marinevibrator (not shown in FIG. 9) and reflected by the sea floor and thegeologic formations lying beneath. Such instruments may include anaccelerometer 100 in accordance with at least some of the embodimentsdescribed herein sensitive to accelerations of the fluid particlesinduced by the acoustic seismic signal. In some embodiments, suchinstruments may also include a hydrophone sensitive to acoustic pressurefluctuations comprising the seismic signal. The component of velocity ofsuch fluid particles along the axis of sensitivity of accelerometer 100may be obtained by time integration of the output signals of theaccelerometer. By suitably combining such velocity data with the outputfrom the hydrophone, artifacts in the seismic signal from, for example,reflections of the signal from the sea surface may be substantiallyreduced.

FIG. 10 shows a flow chart of a method 1000 for measuring a motion of abody. In block 1002 a first cantilever portion of a sensing element isdeflected in a direction opposite a first acceleration direction of thebody. A second cantilever portion of the sensing element is deflected inthe direction opposite the first acceleration direction of the body inblock 1004. In block 1006 a first voltage is created having a firstpolarity, the first voltage being created across electrical leads inresponse to the deflecting of the cantilever portions. The firstcantilever portion is deflected along a direction opposite a secondacceleration direction of the body in block 1008, the secondacceleration direction being opposite the first acceleration direction.In block 1010 the second cantilever portion is deflected along adirection opposite the second acceleration direction of the body, and inblock 1012 a second voltage is created having a second polarity, thesecond polarity opposite the first polarity, the second voltage beingcreated across leads responsive to the deflecting of the cantileverportions. Method 1000 ends at block 1014. It is noted that although theflow chart depicts the blocks of the method in serial fashion, someoperations may be executed substantially simultaneously, and the serialdepiction does not indicate that the described operations arenecessarily to occur sequentially in time.

In accordance with an embodiment, a geophysical data product indicativeof certain properties of the subsurface rock may be produced from themeasuring motion of the body. The geophysical data product may includeprocessed seismic or electromagnetic geophysical data and may be storedon a non-transitory, tangible computer-readable medium. The geophysicaldata product may be produced offshore (i.e. by equipment on a vessel) oronshore (i.e. at a facility on land) either within the United States orin another country. If the geophysical data product is produced offshoreor in another country, it may be imported onshore to a facility in theUnited States. Once onshore in the United States, geophysical analysis,possibly including further data processing, may be performed on the dataproduct.

References to “one embodiment,” “an embodiment,” “a particularembodiment,” and “some embodiments” indicate that a particular elementor characteristic is included in at least one embodiment of theinvention. Although the phrases “in one embodiment,” “an embodiment,” “aparticular embodiment,” and “some embodiments” may appear in variousplaces, these do not necessarily refer to the same embodiment.

The above discussion is meant to be illustrative of the principles andvarious embodiments of the present invention. Numerous variations andmodifications will become apparent to those skilled in the art once theabove disclosure is fully appreciated. For example, multipleaccelerometers 100 may be deployed in embodiments in which therespective sensitivity axes are individually oriented to resolvedifferent components of the applied acceleration. It is intended thatthe following claims be interpreted to embrace all such variations andmodifications.

What is claimed is:
 1. A streamer comprising: a cable; a hydrophonecoupled to the cable, the hydrophone sensitive to acoustic pressurefluctuations; and are accelerometer coupled to the cable, theaccelerometer comprising: a first piezoelectric element having a firstpolarization, the first piezoelectric element defines an upper surface;a second piezoelectric element having a second polarization, the secondpiezoelectric element defines a lower surface parallel to the uppersurface of the first piezoelectric element, and the first polarizationaligned with the second polarization; a first mounting plate thatdefines a first aperture; the first and second piezoelectric elementsextend through the first aperture such that the first mounting platetransects the first and second piezoelectric elements, the piezoelectricelements define a first cantilever portion on a first side of the firstmounting plate, and the piezoelectric elements define a secondcantilever portion on a second side of the first mounting plate oppositethe first side; wherein the first mounting plate defines a peripherycomprising: a first arcuate curve portion; a second arcuate curveportion disposed on opposite first arcuate curve portion; a first chordconnecting a first end of the first arcuate curve portion with a firstend of the second arcuate curve portion; and a second chord connecting asecond end of the first arcuate curve portion with a second end of thesecond arcuate curve portion.
 2. The streamer of claim 1: wherein theupper surface of the first piezoelectric element defines a first plane;and wherein the lower surface of the second piezoelectric elementdefines a second plane parallel to the first plane.
 3. The streamer ofclaim 2 wherein the first mounting plate defines a first surface thatdefines a third plane, and wherein the third plane is perpendicular tothe first and second planes.
 4. The streamer of claim 1 furthercomprising: a second mounting plate that defines a second aperture, thesecond mounting plate spaced apart from the first mounting plate, andthe second mounting plate parallel to the first mounting plate; whereinthe first and second piezoelectric elements extend through the secondaperture such that the second mounting plate transects the first andsecond piezoelectric elements; and wherein the first cantilever portionis disposed distally to the first mounting plate and the secondcantilever portion is disposed distally to the second mounting plate. 5.The streamer of claim 1 wherein the first mounting plate comprises ametallic member disposed abutting the first piezoelectric element, thefirst piezoelectric element bonded to the metallic member.
 6. Thestreamer of claim 5 further comprising solder that electrically andmechanically couples the metallic member and a metallized layer on theupper surface of the first piezoelectric element.
 7. The streamer ofclaim 1 wherein the first and second piezoelectric elements arecomprised of piezoelectric materials selected from the group consistingof: lead zirconate titanate (PZT); barium titanate; bismuth titanate;lead titanate; berlinite; and polyvinylidene fluoride (PVDF).
 8. Thestreamer of claim 1 wherein the first mounting plate has a substrate ofnon-conductive material.
 9. The streamer of claim 1 wherein the secondpolarization has a sign opposite a sign of the first polarization. 10.The streamer of claim 9 further comprising the accelerometer configuredto produce an electrical signal in response to an acceleration componentin a direction of sensitivity perpendicular to the upper surface, andthe accelerometer configured to produce substantially no electricalsignal in response to an acceleration component orthogonal to thedirection of sensitivity.
 11. The streamer of claim 1 further comprisingthe accelerometer configured to produce an electrical signal in responseto an acceleration component in a direction of sensitivity perpendicularto the upper surface, and the accelerometer is configured to producesubstantially no electrical signal in response to pressure acting on theaccelerometer.
 12. The streamer of claim 1 further comprising: ametallic member comprising a sheet of conductive material, a surface ofthe metallic member defines a first rectangle; the first piezoelectricelement coupled to a first side of the metallic member; the secondpiezoelectric element coupled to a second side of the metallic member,the second side opposite the first side; wherein the upper surface ofthe first piezoelectric element defines a second rectangle congruent tothe first rectangle; and wherein the lower surface of the secondpiezoelectric element defines a third rectangle congruent to the firstrectangle.
 13. The streamer of claim 12 further comprising: a secondmounting plate that defines a second aperture, the second mounting platespaced apart from the first mounting plate, and the second mountingplate parallel to the first mounting plate; wherein the first and secondpiezoelectric elements extend through the second aperture such that thesecond mounting plate transects the first and second piezoelectricelements; wherein the first cantilever portion is disposed distally tothe first mounting plate and the second cantilever portion is disposeddistally to the second mounting plate; and wherein the first and secondmounting plates are contrasted of a substrate of non-conductivematerial.
 14. The streamer of claim 13 further comprising: a housingthat defines a first end, a second end opposite the first end, aninterior volume, and a circular cross-section; a cap coupled to andoccluding the first end of the housing; the mounting plates,piezoelectric elements, and metallic member disposed within the interiorvolume; an end cap coupled to and partially occluding the second end; afirst electrical lead that extends through the end cap, the firstelectrical lead electrically coupled to the first piezoelectric element;and a second electrical lead that extends through the end cap, thesecond electrical lead electrically coupled to the second piezoelectricelement.
 15. A sensor streamer comprising: a cable; a hydrophone coupledto the cable, the hydrophone sensitive to acoustic pressurefluctuations; and an accelerometer coupled to the cable, theaccelerometer comprising: a first means for creating an electricalcharge responsive to deflection, the first means for creating has afirst polarization; a second means for creating an electrical chargeresponsive to deflection, the second means for creating has a secondpolarization aligned with the first polarization; a conducting platethat defines a first side and a second side opposite the first side afirst means for adhering the first means for creating to the first sideof the conducting plate; a second means for adhering the second meansfor creating to the second side of the conducting plate; a firstmounting plate that defines a first aperture; the first and second meansfor creating extend through the first aperture such that the firstmounting plate transects the first and second means for creating, andthe first and second means for creating define a first cantileverportion on a first side of the first mounting plate and a secondcantilever portion on a second side of the first mounting plate oppositethe first side; wherein the first mounting plate defines a peripherycomprising: a first arcuate curve portion; a second arcuate curveportion disposed on opposite first arcuate curve portion; a first chordconnecting a first end of the first arcuate curve portion with a firstend of the second arcuate curve portion; and a second chord connecting asecond end of the first arcuate curve portion with a second end of thesecond arcuate curve portion.
 16. The streamer of claim 15 furthercomprising: a second mounting plate that defines a second aperture, thesecond mounting plate spaced apart from the first mounting plate, andthe second mounting plate parallel to the first mounting plate; whereinthe first and second means for creating extend through the secondaperture such that the second mounting plate transects the first andmeans for creating; and wherein the first cantilever portion is disposeddistally to the first mounting plate and the second cantilever portionis disposed distally to the second mounting plate.
 17. The streamer ofclaim 15 wherein the first and second means for creating are comprisedof piezoelectric materials selected from the group consisting of: leadzirconate titanate (PZT); barium titanate; bismuth titanate; leadtitanate; berlinite; and polyvinylidene fluoride (PVDF).
 18. Thestreamer of claim 15 further comprising: a means for housing themounting plate and the first and second means for creating; a means foroccluding a first end of the means for housing; a means for partiallyoccluding a second end of the means for housing; a first electrical leadthat extends through the means for partially occluding, the firstelectrical lead electrically coupled to the first means for creating;and a second electrical lead that extends through the means forpartially occluding, the second electrical lead electrically coupled tothe second means for creating.